Confidence limits for contribution plots

Multiscale Multiblock Batch Monitoring: Sensor and Process Drift and Degradation

“…Conlin et al proposed a number of approaches for obtaining confidence limits for the individual variable contributions. The underlying premise is that the data follow a normal distribution and hence that the following limits are applicable: c t ± z α/2 ·σ̂ c where z α/2 is the corresponding standard normal deviate and σ̂ c is the estimated standard deviation.…”

Multiscale Multiblock Batch Monitoring: Sensor and Process Drift and Degradation

“…Conlin et al proposed a number of approaches for obtaining confidence limits for the individual variable contributions. The underlying premise is that the data follow a normal distribution and hence that the following limits are applicable: c t ± z α/2 ·σ̂ c where z α/2 is the corresponding standard normal deviate and σ̂ c is the estimated standard deviation.…”

Fault Localization in Batch Processes through Progressive Principal Component Analysis Modeling

“…As the abnormal batch is detected, SPE contribution plot at this time point is produced to see the contributions from different variables as shown in Figure . The 99% control limits for the contributions from all variables are also computed and plotted as the dotted line . It can be easily seen that variable no.…”

“…The 99% control limits for the contributions from all variables are also computed and plotted as the dotted line. 32 It can be easily seen that variable no. 3, substrate feed rate, and variable no.…”

Monitoring roughness and edge shape on semiconductors through multiresolution and multivariate image analysis

“…Figure 11 shows the e contributions to the residuals of all the pixels along the length of a row within the same edge considered in Figure 10. If the e contribution of a pixel exceeds one of the confidence limits,28 this is an indication that a surface imperfection is localized on that pixel. Following this rationale, several imperfections are detected by the contributions plot of Figure 11 around pixel columns 10 to 40, around column 100, and around column 135.…”

Multiscale Multiblock Batch Monitoring: Sensor and Process Drift and Degradation

“…Conlin et al proposed a number of approaches for obtaining confidence limits for the individual variable contributions. The underlying premise is that the data follow a normal distribution and hence that the following limits are applicable: c t ± z α/2 ·σ̂ c where z α/2 is the corresponding standard normal deviate and σ̂ c is the estimated standard deviation.…”

Fault Localization in Batch Processes through Progressive Principal Component Analysis Modeling

“…As the abnormal batch is detected, SPE contribution plot at this time point is produced to see the contributions from different variables as shown in Figure . The 99% control limits for the contributions from all variables are also computed and plotted as the dotted line . It can be easily seen that variable no.…”

“…The 99% control limits for the contributions from all variables are also computed and plotted as the dotted line. 32 It can be easily seen that variable no. 3, substrate feed rate, and variable no.…”

Monitoring roughness and edge shape on semiconductors through multiresolution and multivariate image analysis

“…Figure 11 shows the e contributions to the residuals of all the pixels along the length of a row within the same edge considered in Figure 10. If the e contribution of a pixel exceeds one of the confidence limits,28 this is an indication that a surface imperfection is localized on that pixel. Following this rationale, several imperfections are detected by the contributions plot of Figure 11 around pixel columns 10 to 40, around column 100, and around column 135.…”

Multiscale Multiblock Batch Monitoring: Sensor and Process Drift and Degradation

“…Conlin et al proposed a number of approaches for obtaining confidence limits for the individual variable contributions. The underlying premise is that the data follow a normal distribution and hence that the following limits are applicable: c t ± z α/2 ·σ̂ c where z α/2 is the corresponding standard normal deviate and σ̂ c is the estimated standard deviation.…”

Fault Localization in Batch Processes through Progressive Principal Component Analysis Modeling

“…As the abnormal batch is detected, SPE contribution plot at this time point is produced to see the contributions from different variables as shown in Figure . The 99% control limits for the contributions from all variables are also computed and plotted as the dotted line . It can be easily seen that variable no.…”

“…The 99% control limits for the contributions from all variables are also computed and plotted as the dotted line. 32 It can be easily seen that variable no. 3, substrate feed rate, and variable no.…”

Monitoring roughness and edge shape on semiconductors through multiresolution and multivariate image analysis

“…Figure 11 shows the e contributions to the residuals of all the pixels along the length of a row within the same edge considered in Figure 10. If the e contribution of a pixel exceeds one of the confidence limits,28 this is an indication that a surface imperfection is localized on that pixel. Following this rationale, several imperfections are detected by the contributions plot of Figure 11 around pixel columns 10 to 40, around column 100, and around column 135.…”